## Knowledge Expectations for METR 4133 Atmospheric Dynamics III : Mid-Latitude Synoptic-Scale Dynamics

Purpose: This document describes the principal concepts, technical skills, and fundamental
understanding that all students are expected to possess upon completing METR 4123, Mid-Latitude
Synoptic-Scale Dynamics. Individual instructors may deviate somewhat from the specific topics and
order listed here.

Pre-requisites: Grade of C or better in METR 3123, METR 3223.

Upon entering this course, students should have a working knowledge of real and apparent forces,
the equations of motion and their simplified forms, coordinate systems, vorticity, circulation,
angular momentum, moist and dry thermodynamics, and static stability.

Goals of the Course: This course combines concepts from kinematics, dynamics and thermodynamics to
characterize the synoptic-scale atmosphere, with emphasis on quasi-geostrophic and baroclinic
instability theory as the basis for understanding the structure, movement and evolution of
extra-tropical weather systems including fronts and jets. Linear theory is used to describe a
variety of atmospheric waves and to assess their role and relative importance in synoptic-scale
meteorology.

Topical Knowledge Expectations

I. Kinematics of the Wind and Pressure Fields
• Understand the mathematical definition of ridges, troughs, highs, lows, cols and be able to
express atmospheric wave motion in analytic form with an understanding of phase speed, wavelength,
wave number, amplitude and phase.
• Understand and be able to apply formulae for the movement of pressure systems, and be able to
explain their formation and intensification.
• Understand the expansion of the wind field about a point using Taylor series, rotational
invariance, the physics and mathematics of pure fluid translation, divergence, rotation, and
deformation in Cartesian and natural coordinates.
• Understand and be able to apply the concepts of streamfunction and velocity potential to two-
dimensional flow.

II. Quasi-Geostrophic and Baroclinic Instability Theory: Extratropical Cyclones
• Understand the term “quasi-geostrophic” as applied to the synoptic scale and be able to apply
scale analysis to the thermodynamic and vorticity equations, via quantitative waveform-based
methods, to arrive at the quasi-geostrophic thermodynamic and vorticity equations.
• Understand how the vertical-p velocity relates to vertical-z velocity and be able to use the
continuity equation to determine the vertical velocity at any level.
• Understand physically and mathematically the ageostrophic wind and its linkage with vertical
motion, vertical motion in the context of horizontal motion in the presence of orography, and be
able to compute vertical motion from the thermodynamic energy equation.
• Understand the methodology for deriving the quasi-geostrophic omega and height tendency equations
and be apply them to determine height tendency and vertical motion fields. Further, understand how
the atmosphere responds to perturbations to restore a state of quasi-geostrophic balance.
• Understand the concept of potential vorticity, be able to derive and explain physically the
governing equation, and be able to apply potential vorticity in the context of synoptic-scale
dynamics.